Calculating Velocity of Sphere on Inclined Plane

• moondawg
In summary, the conversation discusses a scenario where a large sphere is rolling without slipping on a horizontal surface and then approaches a 25 degree incline. The sphere has a constant translational speed of 10m/s, mass of 25 kg, and a radius of 0.2m. The moment of inertia of the sphere about its center of mass is given by I=2mr^2/5. The question is to calculate the sphere's velocity as it leaves the top of the incline. The person attempting the solution added the translational and rotational kinetic energies, as well as the potential energy (mgh) to find the total kinetic energy. However, they realize their calculated velocity of 15.53 m/s cannot
moondawg

Homework Statement

A large sphere rolls wothout slipping across a horizontal surface. The sphere has a constant translational speed of 10m/s,mass of 25 kg, radius of .2m. The moment of inertia of the sphere about its center of mass is I=2mr2/5. The sphere approaches a 25 degree incline of height 3m as shown above and rolls up the incline without slipping. Calculate the spheres velocity just as it leaves the top of the incline.

The Attempt at a Solution

I found total kinetic energy by adding translational kin enery, rotational kin energy and (mgh)... i got 3015J and then set that number equal to the equation for kin energy (1/2mv2) and found my new v and got 15.53 m/s but that can't be correct bc if its initial vel as it was going toward the ramp was 10 m/s then why would it speed up if its going up a ramp? idk what i did wrong pleaseee help.!

moondawg said:
I found total kinetic energy by adding translational kin enery, rotational kin energy and (mgh)...
Why did you add mgh? Explain exactly what you did.

1. What is the formula for calculating velocity of a sphere on an inclined plane?

The formula for calculating velocity of a sphere on an inclined plane is v = √(2ghsinθ), where v is the velocity, g is the acceleration due to gravity, h is the height of the inclined plane, and θ is the angle of inclination.

2. How do you determine the acceleration due to gravity in this calculation?

The acceleration due to gravity is a constant value of 9.8 m/s² and can be determined through experiments or obtained from reference materials.

3. Can this formula be used for any inclined plane?

Yes, this formula can be used for any inclined plane as long as the angle of inclination is known and the sphere is rolling without slipping.

4. What factors can affect the velocity of the sphere on an inclined plane?

The velocity of the sphere on an inclined plane can be affected by the angle of inclination, mass of the sphere, and the coefficient of friction between the sphere and the inclined plane.

5. What are some real-life applications of calculating velocity of a sphere on an inclined plane?

Calculating the velocity of a sphere on an inclined plane can be helpful in understanding the motion of objects on ramps or hills, such as in roller coasters, car ramps, or playground slides. It can also be used in studying the behavior of rolling objects in physics experiments or in designing machinery that involves inclined planes.

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